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Experienced Settlers of Catan players know that the answer to this question will vary based on many board setup factors such as resource productivity, 2:1 ports, whether you can corner the market for one resource and thus trade for the resource you lack, etc. For the purposes of this question, let's exclude such factors, and consider the middle case where there are no obvious 2:1 port setups, nobody can corner a market, and the distribution of production is a middling 10 dots each for the brick and ore, 13 dots each for wood and grain, and 12 dots for sheep.

3 Answers
3

This will depend tremendously on the situation, but it's worth learning some generalities:

If you are playing with just the base set:

brick and wood are completely identical as everything that needs one wood also needs one brick (roads and settlements).

Wheat is completely superior to wool/sheep as it is also needed for cities in addition to everything wool is needed for.

Wheat and Ore are about tied as you need 1 wheat for a settlement and no ore and 3 ore for a city and 2 wheat. My experience is that wheat is slightly better as the ability to continue building settlements is usually worthy a slightly diminished city building capacity caused by an increase in wheat and decrease in your ore.

Anyone who has played 4+ games of Settlers knows that you need a variety of resources to win, although there are widely differing ways to get them, so there's no such thing as 'the best' resource as the distribution is so situational to the island layout, what other players have, what development cards and resources you have, and what everybody needs. However, wheat is essential to virtually any strategy, ore is needed for a city/development card strategy, wood and brick are necessary in at least small amounts for any expansion via new settlements and roads, and wool is overall probably least useful.

That is, until nobody goes for wool but you, making you the one who can build settlements faster and extort ridiculous prices from your adversaries for it until you take an early 3 point lead for a decisive win. As I said, it's all relative. :D

Your answer is quite good though I would suggest one small change: brick and wood are NOT completely identical because there are 4 wood hexes and 3 brick hexes. Brick (10 dots) is more valuable than wood (13 dots) from the scarcity/trading perspective in the median scenario. Your comments about wheat are terrific, and are further bolstered when you consider having a large bunch (say, 12) identical cards in your hand and what you can do with them on your turn, with or without a 3:1 port. A reasonable argument can be made that ore is more valuable than wheat (scarcity) but I don't agree with it.
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Joe GoltonJan 26 '12 at 22:58

1

Really good answer, and coupled with Joe's comment there it becomes an amazing answer! Lots of things I hadn't really thought about before.
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thesunneversetsJan 27 '12 at 11:16

The value of resources depends on the stage of the game, and your strategy. A very typical strategy is to expand early until you have 3 or 4 settlements, and then focus on upgrading to cities while continuing to expand only when convenient. If this is your goal, brick and wood will be important in the beginning, and ore important in the late game, with wool and wheat somewhere in between throughout. On the other hand, it's possible to play a strong game without much emphasis on expansion, by focusing instead on cities and development cards, and only expanding when convenient. The most important things are to have a strategy and make choices consistent with your strategy, however there is no "best strategy" and thus no "best resource".

If you are going for a one resource strategy(a 2:1 port and multiple good hexes), then Ore is definitely the best. With only one resource, settlements/roads will be expensive to build. This leaves cities as your main early game expansion option. Since you need 3 ore to 2 corn, ore is the better choice.

If you are just going for a general game, then you want all the resources, but sheep is definitely less important than corn. (As it is not required for cities.) You can make do without sheep by trading for it when you need a settlement, while wood/bricks are needed in large numbers for roads/settlements and corn/ore are needed for cities and development cards in large amounts.

Note that you can win a game without wood/bricks (2 cities, largest army and 4 VP cards) But you cannot win a game without ore. (5 settlements and longest road=7VP)